Titlebook: Numerical Methods for Solving Discrete Event Systems; With Applications to Winfried Grassmann,Javad Tavakoli Textbook 2022 The Editor(s) (i

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2730-650X d aid practitioners significantly to solve their problems. This book also provides an interesting approach to teaching courses of stochastic processes.. .?.978-3-031-10084-0978-3-031-10082-6Series ISSN 2730-650X Series E-ISSN 2730-6518

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Basic Concepts and Definitions, chapter provides the basic mathematical tools for this endeavor. We thus describe what a system is, and how to work with Markov chains. Since our systems are stochastic, we also review random variables and their distributions. Many systems covered in this book are in fact queueing systems, and we t

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Systems with Events Generated by Poisson or by Binomial Processes,waiting line to another, as well as departures. However, the rate of the process may depend on the state of the system. We will also discuss systems where the events are generated by binomial processes. Models include the ././1 queue, a tandem queue and several other examples.

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Systems with Events Created by Renewal Processes,t random variables. Technically, this means that the process generating the event type in question forms a renewal processes, with the events being the renewals. We call a discrete event system a . if the times between events are renewal processes. Here, we include renewal processes that can be susp

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Execution Times, Space Requirements, and Accuracy of Algorithms,d, and how accurate are the results. All these criteria will be covered in this chapter. The time needed for finding an answer is covered under the heading of ., and the requirement for memory needed to execute the algorithm is covered under the heading of .. Sources of inaccuracies include data err

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Moving toward the Statistical Equilibrium,d if they exist, whether or not they depend on the initial state. These are the questions addressed in this chapter. The tools to resolve these questions include the classification of states, as well as the characterization of transient solutions by eigenvalues.

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Equilibrium Solutions of Markov Chains and Related Topics,fference between the equilibrium equations of DTMCs and CTMCs. In particular, we discuss the state elimination method, a variant of Gaussian elimination that has probabilistic interpretation. This then leads to the fundamental matrix and its use. Iterative methods are also described, and illustrated